Modified Duration Calculator

Formula

To calculate the Modified Duration (MD):

\[ MD = \frac{MCD}{1 + \frac{YTM}{n}} \]

Where:

\(MD\) is the Modified Duration
\(MCD\) is the Macaulay Duration
\(YTM\) is the Yield to Maturity
\(n\) is the Number of Periods per Year

Modified Duration Definition

Modified duration is defined as the ratio of the change in the value of a security to the change in the value of the interest rate. It measures the sensitivity of the price of a bond to changes in interest rates, providing an estimate of how much the price of the bond will change for a 1% change in yield.

Example Calculation

Let's assume the following values:

Macaulay Duration (\(MCD\)) = 5 years
Yield to Maturity (\(YTM\)) = 0.06 (or 6%)
Number of Periods per Year (\(n\)) = 2

Using the formula:

\[ MD = \frac{5}{1 + \frac{0.06}{2}} = \frac{5}{1 + 0.03} = \frac{5}{1.03} \approx 4.8544 \]

The modified duration is approximately 4.8544 years.